# Group invariant machine learning for Calabi-Yau polyhedra

### Dr Daniel Platt

### David Sheard

### Dr Benjamin Aslan

#### Abstract

There are many group invariant machine learning models, i.e. learnable functions that give the same output if the input is acted on by a group. One novel approach is using fundamental domain projections - an approach which is particularly useful if the group which acts is very large [1]. There are many large string theory datasets with large symmetry groups, which make good benchmarks for group invariant machine learning models. One such example is the Kreuzer-Skarke dataset of Calabi-Yau three-folds coming from reflexive polyhedra and their Hodge numbers [2].

In this project, we will apply invariant machine learning via fundamental domain projections to the Kreuzer-Skarke dataset and compare this with other group invariant machine learning techniques (e.g. data augmentation and deep sets), as well models that are not group invariant.

**References**

[1] *Group invariant machine learning by fundamental domain projections**, *Benjamin Aslan, Daniel Platt, David Sheard, arXiv 2022

[2] __Calabi-Yau data__